A measuring device of this type is described in DE 26 42 044 B1. Static and dynamic stresses of a roller bearing are determined in an elaborate form by means of strain gages. One characteristic variable for the determination of the stress of the bearing is the elastic deformation of the bearing itself. The deformation of a bearing ring with rolling contact under loads is, as a rule, detected by the strain gages. For this purpose, the strain gages are fastened directly to the stressed bearing ring. This sensor system needs installation space on the bearing and is to be protected against environmental influences. Arrangements of this type are therefore complicated as a rule.